Modified Scaled Hierarchical Equation of Motion Approach for the Study of Quantum Coherence in Photosynthetic Complexes

Abstract

We present a detailed theoretical study of the transfer of electronic excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein complex, using the newly developed modified scaled hierarchical approach (Shi, Q.; et al. J. Chem. Phys. 2009, 130, 084105). We show that this approach is computationally more efficient than the original hierarchical approach. The modified approach reduces the truncation levels of the auxiliary density operators and the correlation function. We provide a systematic study of how the number of auxiliary density operators and the higher-order correlation functions affect the exciton dynamics. The time scales of the coherent beating are consistent with experimental observations. Furthermore, our theoretical results exhibit population beating at physiological temperature. Additionally, the method does not require a low-temperature correction to obtain the correct thermal equilibrium at long times.

Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy

“…To lower the temperature (β¯ω 0 ≈ 10), one may need to employ numerical techniques to accelerate calculations. [89][90][91][92] It should be noted that dynamical behavior of the system does not change so much once the temperature becomes low enough compared with the characteristic frequency of the system (such as ω u ), since the thermal excitation becomes so small that the fluctuation does not play any role for electronic excitation at very low temperature. So, in practice, we do not have to lower the temperature below β¯ω u ≈ 10 for ω 0 ω u .…”

“…Inclusions of multimode are computationally very expensive, and therefore one has to employ a variety of numerical techniques developed for HEOM approach to accelerate numerical calculations. 46,47,[89][90][91][92] Here, we assumed that the primary oscillator modes are harmonic. However, if we employ a less reduced density matrix in which the bath (x n j ) modes are eliminated and we still keep the oscillator coordinates q j , we can relax this limitation.…”

Effect of strong electron correlation on the efficiency of photosynthetic light harvesting

“…Non-Markovian effects from the environment can also be added to the quantum Liouville equation (for example, refer to Ref. [10]); however, they will not qualitatively change the effect of strong electron correlation within chromophores on energy-transfer efficiency.…”

“…Recent spectroscopic experiments [1][2][3] and theoretical models [4][5][6][7][8][9][10][11][12][13], provide evidence that efficient light harvesting in nature occurs by a quantum mechanism involving sustained electronic coherence [14] and entanglement [15,16] between chromophores. While the chromophores are chlorophyll molecules containing large networks of conjugated carbon bonds that surround a charged magnesium ion, they have largely been represented in theoretical studies [4][5][6][7][8][9][10][11][12][13] by one-electron models that neglect the effects of electron correlation and entanglement within chromophores. Two advanced methods in electronic structure, density-matrix renormalization group [17] and two-electron reduceddensity-matrix theory [18,19], have recently shown that networks of conjugated bonds as in acene chains [17,20], acene sheets [20], and chlorophyll are associated with polyradical character that cannot be adequately described without a strongly correlated many-electron quantum model.…”

Simulated two-dimensional electronic spectroscopy of the eight-bacteriochlorophyll FMO complex

“…To tackle this problem, a methodology referred to as hierarchical equation of motion (HEOM) has been developed by Tanimura and co-workers [19,20]; a high temperature approximation (HTA) of HEOM has also been developed by Ishizaki and co-workers to describe the EET dynamics in a model dimer [21,22]. The HEOM has already been implemented in calculating the excitonic transfer dynamics of photosynthetic proteinpigment complexes [23][24][25][26][27] and more recently it is also used within simulations of the linear and 2D electronic spectra of the above mentioned systems [28][29][30].…”